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Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality
Synchronization is an important behavior that characterizes many natural and human made systems that are composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the com...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7823721/ https://www.ncbi.nlm.nih.gov/pubmed/33383735 http://dx.doi.org/10.3390/e23010036 |
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author | Muolo, Riccardo Carletti, Timoteo Gleeson, James P. Asllani, Malbor |
author_facet | Muolo, Riccardo Carletti, Timoteo Gleeson, James P. Asllani, Malbor |
author_sort | Muolo, Riccardo |
collection | PubMed |
description | Synchronization is an important behavior that characterizes many natural and human made systems that are composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, with the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework for tackling synchronization problems. Using this method, it has been shown that, for a class of models, synchronization in strongly directed networks is robust to external perturbations. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Moreover, many empirical networks are also strongly non-normal. Inspired by this latter fact in this work, we address the role of the non-normality in the synchronization dynamics by pointing out that standard techniques, such as the MSF, may fail to predict the stability of synchronized states. We demonstrate that, due to a transient growth that is induced by the structure’s non-normality, the system might lose synchronization, contrary to the spectral prediction. These results lead to a trade-off between non-normality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization. |
format | Online Article Text |
id | pubmed-7823721 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-78237212021-02-24 Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality Muolo, Riccardo Carletti, Timoteo Gleeson, James P. Asllani, Malbor Entropy (Basel) Article Synchronization is an important behavior that characterizes many natural and human made systems that are composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, with the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework for tackling synchronization problems. Using this method, it has been shown that, for a class of models, synchronization in strongly directed networks is robust to external perturbations. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Moreover, many empirical networks are also strongly non-normal. Inspired by this latter fact in this work, we address the role of the non-normality in the synchronization dynamics by pointing out that standard techniques, such as the MSF, may fail to predict the stability of synchronized states. We demonstrate that, due to a transient growth that is induced by the structure’s non-normality, the system might lose synchronization, contrary to the spectral prediction. These results lead to a trade-off between non-normality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization. MDPI 2020-12-29 /pmc/articles/PMC7823721/ /pubmed/33383735 http://dx.doi.org/10.3390/e23010036 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Muolo, Riccardo Carletti, Timoteo Gleeson, James P. Asllani, Malbor Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality |
title | Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality |
title_full | Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality |
title_fullStr | Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality |
title_full_unstemmed | Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality |
title_short | Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality |
title_sort | synchronization dynamics in non-normal networks: the trade-off for optimality |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7823721/ https://www.ncbi.nlm.nih.gov/pubmed/33383735 http://dx.doi.org/10.3390/e23010036 |
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